CN100385459C - An Image Watermarking Method Based on Finite Ridgelet Transform - Google Patents

Abstract

An image watermarking method based on finite ridgelet transform belongs to the technical field of information security, and in particular relates to finite ridgelet transform theory and image digital watermarking technology. First divide the image into prime p blocks, and generate a watermark sequence w={w _i |w _i ∈ {-1, 1}, 0≤i≤L-1} with a length of L=p-1; then Each block is subjected to finite ridgelet transformation; search for a direction with the largest energy in the transformed ridgelet domain, and embed the watermark in this direction; the formula used for watermark embedding takes into account the sensitivity of the human eye to changes in different directions The intensity of watermark embedding is different in different directions; the same watermark is embedded in each image block, which realizes the localization of watermark. The image watermark method provided by the invention has good watermark invisibility, high degree of discrimination of relevant detection values during watermark detection, robustness to conventional image processing operations, and especially can resist image clipping attacks.

Description

An Image Watermarking Method Based on Finite Ridgelet Transform

technical field

An image watermarking method based on finite ridgelet transform belongs to the technical field of information security, and in particular relates to finite ridgelet transform theory and image digital watermarking technology.

Background technique

The rapid development of digital technology and network technology has changed people's life in many ways. The exchange of multimedia information based on computer and network provides a convenient way for the use and dissemination of digital works, which makes digital works have great advantages compared with traditional works. However, the advent of the network information age also poses new challenges to copyright protection, and the traditional information encryption technology can no longer meet the needs of practical applications. Digital watermarking technology is an emerging interdisciplinary application technology, which absorbs ideas and theories from many disciplines. Simply put, digital watermarking technology is an information hiding technology. Its basic idea is to embed secret information in digital products such as digital images, audio and video, in order to protect the copyright of digital products, prove the authenticity of products, and track piracy. conduct or provide additional information about a product. Digital watermarking technology has become the fastest-growing hot technology in the field of multimedia information security research, and is being highly concerned by international academic circles and business circles. Therefore, no matter from the theoretical point of view or the application point of view, it is of great academic and economic significance to carry out research on digital watermarking technology. For details, see the literature: J.Cox, L.Miller, A.Bloom, "Digital Watermarking", Morgan Kaufmann, 2003 and the literature: Sun Shenghe, Lu Zheming, Niu Xiamu, "Digital Watermarking Technology and Application", Science Press, 2004 wait.

Image digital watermarking technology is an important research field of digital watermarking technology. Since the digital watermarking technology was proposed in the 1990s, various image watermarking algorithms have emerged continuously. The more common image watermark embedding algorithms can be divided into three categories:

(1) Spatial domain watermark embedding algorithm. Early research on digital watermarking was basically based on the space domain, the algorithm is relatively simple, and the real-time performance is strong, but it is not as robust as the transform domain algorithm. See literature for details: R.G.Van Schyndel, A.Z.Trickle, N.Mee, C.F.Osborne, "A Digital Watermark", Proceedings of IEEE International Conference on Image Processing, 1994, 2:86-90 and literature: Zhou Lijun, Zhou Yuanhua, Zhi Zheng, " Multiple image watermarking based on m-sequence", Journal of Shanghai Jiaotong University, 2001, 35(9): 1317-1320, etc.

(2) Watermark embedding algorithm in DCT domain. Discrete cosine transform (DCT) is one of the most commonly used linear transforms in digital signal processing technology. It is a real transform with good energy compression and decorrelation capabilities. In particular, the JPEG compression standard for digital images is based on DCT. Therefore, DCT has received general attention in digital watermark processing technology. See literature for details: I.J.Cox, J.Kalian, T.Leighton, T.Shamoon, "Secure Spread Spectrum Watermarking for Multimedia", IEEE Trans.on Image Processing.1997, 6(12): 1673-1687 and literature: M.A.Suhail, M.S.Obaidat, "Digital Watermarking-based DCT and JPEG Model", IEEE Trans.onInstrumentation and Measurement, 2003, 52(5): 1640-1647, etc.

(3) DWT domain embedding algorithm. As a mathematical tool, wavelet transform and wavelet analysis are a major breakthrough of Fourier transform and window Fourier transform, and have become the most useful tools for data compression, processing and analysis. The digital watermarking method in the wavelet transform domain combines the advantages of the space-time domain method and the DCT transform domain method, and is the hot spot and the most important research direction of the current digital watermarking algorithm research. See literature: A.Lumini, D.Maio, "A Wavelet-based Image WatermarkingScheme", International Conference on Information Technology: Coding and Computing, March27-29, 2000: 122-127 and literature: S.Tsekeridou, I.Pitas , "Waveleet-based Self-similar Watermarking for Still Images", ISCAS'2000, May 28-31, 2000, 1:220-223 et al.

Wavelet analysis has excellent performance when dealing with one-dimensional piecewise smooth functions, because wavelet is good at capturing the singularity of zero dimension (point). For two-dimensional piecewise smooth signals, such as images, they generally have a one-dimensional heterogeneity, such as the edges of objects composed of smooth curves. Wavelet analysis of linear singularities is not a very good representation tool. In order to overcome the weakness of wavelet in dealing with high-dimensional situations, Candes and Donoho proposed a new multi-scale transformation - ridgelet. Ridgelets can effectively deal with the singularity of lines in two-dimensional space. The finite ridgelet transform is a reversible discrete ridgelet transform, which has many advantages compared with other ridgelet transform discretization schemes. See literature: E.J.Candes, D.L.Donoho, "Ridgelets: A key to higher-dimensional intermittency", Phil.Trans, 1999, 2495-2595 and literature: Minh.N.Do, Martin Vetterli, "The Finite Ridgelet Transform for Image Representation" , IEEE Transactions on Image Processing, 2003, 12(1): 16-28, etc.

Contents of the invention

The task of the present invention is to provide an image watermarking algorithm based on finite ridgelet transform, which has the characteristics of localized watermarking and is robust under normal operations on images.

In order to describe the content of the present invention conveniently, some terms are defined first.

Definition 1. Image. The images mentioned in the present invention all refer to two-dimensional still grayscale images.

Definition 2. Watermark. A sequence containing copyright information embedded in an image. The watermark sequence used in the present invention is a binary bipolar sequence {-1, 1}.

Definition 3. Watermark embedding. It refers to embedding the watermark into the original image by a certain method to obtain the image embedded with the watermark.

Definition 4. Watermark detection. Refers to the detection of a suspicious image to determine whether it contains a watermark.

Definition 5. FRAT. The finite Radon transform is an important part of the finite ridgelet transform. The definition is as follows: The FRAT of a real function f on the finite plane Z _p ² is defined as:

${\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; FRA</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\sqrt{\mathrm{<span\; class="notranslate">\; p</span>}}}\underset{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; l</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ]</span>$

where, L _{k, l} = {(i, j): j = ki+l(mod p), i∈Z _p }, 0≤k≤p, Z _p ={0,1,...,p- 1}.

Definition 6. FBP. The finite reflection projection operator is the inverse transformation of the finite Radon transformation. It is defined as follows:

${\mathrm{<span\; class="notranslate">\; FBP</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\sqrt{\mathrm{<span\; class="notranslate">\; p</span>}}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

Wherein, P _i,j ={(k,l):l=j-ki(mod p), k∈Z _p }∪{(p,i)}.

Definition 7. FRAT coefficient matrix. The FRAT transformation is performed on the matrix of p×p size, and the obtained matrix is the FRAT coefficient matrix. The size of the FRAT coefficient matrix is (p+1)×p. Among them, the p+1 row represents the decomposition into p+1 directions, and the p column represents p coefficients corresponding to p displacements in each direction.

Definition 8. One-dimensional discrete wavelet decomposition. Discrete wavelet transform on one-dimensional discrete signal can decompose the first-level approximate component (representing the low-frequency part of the signal) and the first-level detail component (representing the high-frequency part of the signal). The first-level approximation component can be further decomposed into the second-level approximation component and the second-level detail component, and so on.

Definition 9. Finite ridgelet transform. First, FRAT is performed on the matrix in the air domain to obtain the FRAT coefficient matrix, and then one-dimensional discrete wavelet transform is performed on each row sequence of the FRAT coefficient matrix. The whole process is finite ridgelet transform.

Definition 10. Correlation coefficient. Here refers to the cross-correlation coefficient, which characterizes the degree of correlation between two signals. Its value is between [-1, 1]. The larger the correlation coefficient, the greater the similarity between the two signals.

Definition 11. Detection Threshold. Threshold value for determining whether a watermark exists.

Definition 12. PSNR. Peak Signal to Noise Ratio. A pixel-based test method for measuring image quality.

Detailed technical scheme of the present invention is:

A method for image watermarking based on finite ridgelet transform, comprising watermark embedding and watermark detection process, characterized in that said watermark embedding process comprises the following steps:

Step 1. Generate a watermark sequence w={w _i |w _i ∈{-1, 1}, 0≤i≤L-1} whose length is L=p-1 (p is a prime number).

Step 2. Select the block size p (p=L+1), and divide the original image I into N blocks in total, that is, obtain the block image B _x , 0≤x≤N-1.

Step 3. For each block image, perform the following operations:

Step 3-1. Perform FRAT transformation on the block image B _x , 0≤x≤N-1, to obtain a FRAT coefficient matrix R _x of size (p+1)×p, 0≤x≤N-1.

Step 3-2. Perform one-dimensional discrete wavelet decomposition on each row of the FRAT coefficient matrix R _x to obtain the first layer detail component sequence d _{x, k} , 0≤x≤N-1, 0≤k≤p.

Step 3-3, calculating the energy e z _{, k of the sequence d x , k} ,

${\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

Step 3-4, fix the parameter x, find the largest _ex,m among ex _,k , and the corresponding detail component sequence is dx _,m .

Step 3-5, embed the watermark into the sequence d _{x, m} according to the formula,

d' _{x, m, i} = d _{x, m, i} + α _m βw _i , 0≤i≤p-2

Among them, α _m is the direction sensitivity factor, which reflects the sensitivity of human eyes to different directions. β is an adaptive scaling factor, which is determined by the values of d _{x, m, and i} . The following broken line function can be used to determine β:

$\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; ,</span>& <span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; a</span>}\\ \mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; b</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span>& <span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; a</span>}\end{array}\right.$

Wherein, a, b (a>0, b>0) are constants set artificially.

Step 3-6. According to the above steps, obtain the FRAT coefficient matrix R′ _x after embedding the watermark, perform FBP on it, and obtain the block image B′ _x embedded with the watermark.

Step 4. All the watermark-embedded block images B′ _x are reassembled to obtain the watermark-embedded image I.

The watermark detection process includes the following steps:

Step 1. Obtain the necessary parameters when embedding the watermark. Including block size p and watermark sequence w etc.

Step 2. Divide the image I' to be detected into N blocks, and the block image is: C _x , 0≤x≤N-1.

Step 3. For each block, perform the following operations:

Step 3-1. Perform FRAT transformation on the block image C _x , 0≤x≤N-1, to obtain a FRAT coefficient matrix W _x of size (p+1)×p, 0≤x≤N-1.

Step 3-2. Perform one-dimensional discrete wavelet decomposition on each row of the FRAT coefficient matrix W _x to obtain the first-level detail component sequence d′ _{x, k} , 0≤x≤N-1, 0≤k≤p.

Step 3-3, calculate the energy e′ _{x, k of the sequence d′ x , k} ,

${\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ;</span>$

Step 3-4, fix the parameter x, find the largest e′ x _,m among e′ _x,k , and the corresponding detail component sequence is d′ _x,m , that is, find the position of watermark embedding.

Step 3-5, calculate the correlation coefficient between the sequence d' _{x, m} and the watermark sequence w,

${\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\sqrt{\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}$

Step 4. Average the correlation coefficients z _x obtained from all blocks, where 0≤x≤N-1, to obtain the correlation coefficient z between the entire image and the watermark.

Step 5. Set the detection threshold z _t and determine: if z<z _t , it is determined that the image does not contain a watermark; if z≥z _t , it is determined that the image contains a watermark.

In the above solution, the block size p in step 2 is equal to 17.

It should be noted:

1. The selection of block size is required in step 2 of the embedding process, and p is a prime number, which is necessary. Because FRAT requires that the transformed matrix must be p×p in size and p is a prime number. Due to the limitation of FRAT and this embedding algorithm, the length of the watermark sequence embedded here can only be p.

2. The reason for processing the image into blocks is that the finite ridgelet transform is only suitable for processing the straight line features of the image, and the curved lines in real images are more common than the straight lines. If the finite ridgelet transformation is directly performed on the entire image, the result after transformation is rough and inaccurate for the representation of straight line features. Therefore, similar to many watermarking algorithms in the DCT domain, in the present invention, the image must first be divided into several small blocks. After partitioning, the curved line can be approximated by a straight line in each small block.

3. Find out a detail component sequence with the largest energy, and embed the watermark there. This is because the detail component sequence with the largest energy usually corresponds to a direction with the most linear features in the airspace, and is also an area with rich image texture changes in the airspace. Embedding watermarks into these areas is not easily perceived by human eyes. On the other hand, choosing only one direction to embed the watermark can improve the efficiency and real-time performance of the algorithm.

4. Human eyes have different sensitivity to different directions. It is much more sensitive to changes in the vertical and horizontal directions than to changes in the oblique direction. Since the changes in the vertical and horizontal directions are easy to be noticed, the sequence in these two directions can be excluded when looking for the detail component with the largest energy.

5. The polyline embedding rule used in steps 3-5 of the embedding process is actually a combination of the addition criterion and the multiplication criterion of watermark embedding. Additive criterion is beneficial to obtain high linear correlation value in watermark detection, while multiplicative criterion can realize the adaptability of watermark embedding and has better robustness.

The innovation of the present invention is:

1. Apply finite ridgelet transform to digital watermarking algorithm. Finite ridgelet transform is a new method that has emerged in recent years. It has achieved good results in the fields of line feature detection and image noise reduction and restoration, but there are few literatures on combining it with digital watermarking technology.

2. Search for a detail component sequence with the largest energy of the FRAT coefficient matrix, and only embed the watermark there. It not only ensures that the watermark is embedded in the important area of the image (with linear features or complex texture changes), but also the complexity of the embedding algorithm and detection algorithm is not high.

3. Embed the same watermark into multiple blocks of the image. In this way, on the one hand, the robustness of the algorithm is greatly improved, on the other hand, the watermark detection can only detect one or several blocks, and the speed of the detection process is improved. Another important point is that this method of localized watermarking can resist image cropping attacks, that is, when a piece of image is cut out from the embedded watermarked image, because it still contains several complete blocks, it can detect A watermark exists.

4. The formula for embedding the watermark contains a direction sensitivity factor, which can adjust the embedding strength of the watermark in different directions in combination with the different sensitivities of the human eye to changes in different directions.

5. The polyline rule used when embedding the watermark. The polyline rule combines the advantages of the additive criterion and the multiplicative criterion of watermark embedding, which can make the strength of watermark embedding find a good balance between robustness and invisibility.

Description of drawings

Fig. 1 is a schematic flow chart of the watermark embedding process of the present invention.

Fig. 2 is a schematic flow chart of the watermark detection process of the present invention.

specific embodiment

Adopt the method of the present invention, use Matlab or C language to realize the program of watermark embedding and watermark detection. In the experiment, a 256 grayscale image with a size of 256×256 is used as the test image, the block size p=17, the one-dimensional discrete wavelet is Daubechies-4 wavelet, and the embedding parameters are α _k =1, a=10, b=2 . The detection threshold was set at 0.035. Randomly generate 100 watermarks, and embed them in the original image 100 times to get 100 watermarked images embedded with different watermarks. Perform routine processing on these images, and count their missed detection probability for watermark detection, as shown in the following table:

Image processing performed Probability of missed detection not processed 0% Add Gaussian noise (mean 0, standard deviation 8 grayscale values) 0% 3×3 median filter 11% JPEG compression (quality factor 75%) 7% Random cut 26%

To sum up, the watermarking algorithm provided by the present invention makes full use of the characteristics of the finite ridgelet transform, the method is novel, and it has good robustness and has certain practical value.

Claims (3)

1. the image watermark method based on finite ridgelet transform comprises watermark embedding and watermark detection process, it is characterized in that, described watermark embed process comprises the following step:

Step 1, to produce a length be L=p-1, and p is a prime number, watermark sequence w={w _i| w _i∈ 1,1}, 0≤i≤L-1};

Step 2, the selected block size p that divides, p=L+1 carries out piecemeal to original image I, establishes to be divided into N piecemeal altogether, promptly obtains block image B _x, 0≤x≤N-1;

Step 3, to each block image, carry out following operation:

Step 3-1, to block image B _x, 0≤x≤N-1 does the FRAT conversion, obtains the FRAT matrix of coefficients R of (p+1) * p size _x, 0≤x≤N-1;

Step 3-2, to FRAT matrix of coefficients R _xEach the row do the one-dimensional discrete wavelet decomposition, obtain ground floor details vector sequence d _x, k, 0≤x≤N-1,0≤k≤p;

Step 3-3, sequence of calculation d _{X, k}Energy e _{X, k},

$e_{x,k}=\frac{1}{p-1}\underset{i=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{d}_{x,k,i}^2;$

Step 3-4, preset parameter x find out e _{X, k}A middle maximum e _{X, m}, corresponding details vector sequence is d _{X, m}

Step 3-5, watermark is embedded into sequence d by following formula _{X, m}In,

d _x，m，i′＝d _x，m，i+α _mβw _i，0≤i≤p-2，

Wherein, α _mBe the orientation-sensitive factor, β is the self adaptive pantographic factor, by d _{X, m, i}Value decision, can adopt following polygronal function to decide β:

$\left\{\begin{array}{cc}\mathrm{\&beta;}=b,& \left|d_{x,m,i}\right|\&le;a\\ \mathrm{\&beta;}=\frac{b}{a}\left|d_{x,m,i}\right|,& \left|d_{x,m,i}\right|>a\end{array}\right.$

Wherein, a, b are the artificial constants of setting, and a＞0, b＞0;

Step 3-6, according to above step, obtain the FRAT matrix of coefficients R behind the embed watermark _x', it is FBP, obtain the block image B of embed watermark _x';

Step 4, with the block image B of all embed watermarks _x', be stitched together again, just obtain the image I of embed watermark;

Described watermark detection process comprises the following step:

Step 5, the call parameter when knowing the watermark embedding comprise branch block size p and watermark sequence w;

Step 6, with image I to be detected ' be divided into N piecemeal, block image is: C _x, 0≤x≤N-1;

Step 7, to each block image, carry out following operation:

Step 7-1, to block image C _x, 0≤x≤N-1 does the FRAT conversion, obtains the FRAT matrix of coefficients W of (p+1) * p size _x, 0≤x≤N-1;

Step 7-2, to FRAT matrix of coefficients W _xEach the row do the one-dimensional discrete wavelet decomposition, obtain ground floor details vector sequence d _{X, k}', 0≤x≤N-1,0≤k≤p;

Step 7-3, sequence of calculation d _{X, k}' energy e _{X, k}',

$e_{x,k}^{\&prime;}=\frac{1}{p-1}\underset{i=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{d}_{x,k,i}^{\&prime;2};$

Step 7-4, preset parameter x find out e _{X, k}An e of ' middle maximum _{X, m}', corresponding details vector sequence is d _{X, m}', the position of promptly having found watermark to embed;

Step 7-5, sequence of calculation d _{X, m}' with the related coefficient of watermark sequence w,

$z_x=\frac{\underset{i}{\mathrm{\&Sigma;}}{d}_{x,m,i}^{\&prime;}{w}_i}{\sqrt{\underset{i}{\mathrm{\&Sigma;}}{d}_{x,m,i}^{\&prime;2}\underset{i}{\mathrm{\&Sigma;}}{w}_i^2}},$ 0≤i≤p-2；

Step 8, the related coefficient z that all piecemeals are obtained _x, it is one average that 0≤x≤N-1 does, and obtains the related coefficient z of entire image and watermark;

Step 9, setting detection threshold z _t, and judge: if z＜z _t, the process decision chart picture does not contain watermark; If z 〉=z _t, process decision chart looks like to contain watermark.

2. a kind of image watermark method based on finite ridgelet transform according to claim 1 is characterized in that, divides block size p to equal 17 described in the step 2.

3. a kind of image watermark method according to claim 1 based on finite ridgelet transform, it is characterized in that the one-dimensional discrete small echo is selected the Daubechies-4 small echo for use described in the step 3-2 of described watermark embed process and the step 7-2 of described watermark detection process; Orientation-sensitive factor-alpha described in the step 3-5 of described watermark embed process _m=1, described constant a=10, b=2; The z of detection threshold described in the step 9 of described watermark detection process _tBe set at 0.035.